Existence, Uniqueness and Stability Analysis for a Coupled System of Sequential Hybrid Hilfer Fractional q-Duffing Equations

This paper establishes the existence, uniqueness, and Ulam–Hyers stability of solutions for a novel class of coupled sequential hybrid Hilfer fractional q-Duffing equations. By integrating Dhage’s hybrid structure with generalized Hilfer q-operators, we extend recent results on fractional quantum systems. Existence is proven via Dhage’s fixed point theorem in Banach algebras, while uniqueness follows from the Banach contraction principle with explicit verification of operator invariance. All auxiliary functions satisfy rigorous continuity, boundedness, and Lipschitz conditions, and the solution representation is derived with complete calculation of q-integration constants. The theoretical findings are rigorously validated through a detailed numerical example that explicitly verifies all contraction and stability constants.